Research study on students' conceptions of irrational numbers before entering university is of importance in order that the construction of the real number field introduced at the university level will have the desired effect. The aim of the present study is to analyze the way students approach the question of the existence of irrational numbers.…

This paper explores the dimensions of knowledge and the ways of thinking (procedural or proceptual thinking) adopted by 157 Lebanese students in different grades when defining and identifying irrational numbers when locating them on the number line. It searches for a relation between the performance of the participants and their different grades.…

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…